Which Terms Could Be Used As The Last Term Of The Given Expression To Create A Polynomial Written In Standard Form? Choose Three Correct Answers.Given Expression: \[$-5x^2y^4 + 9x^3y^3 + \square\$\]Options:A. \[$-xy^5\$\]B.

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When it comes to creating a polynomial in standard form, the last term is crucial in determining the overall structure and appearance of the expression. In this article, we will explore the process of selecting the right last term for the given expression −5x2y4+9x3y3+□{-5x^2y^4 + 9x^3y^3 + \square} and identify three correct options.

Understanding the Basics of Polynomials

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The standard form of a polynomial is written with the terms arranged in descending order of exponents, with the highest degree term first.

The Importance of the Last Term

The last term of a polynomial is the term with the lowest degree, and it plays a significant role in determining the overall form of the expression. In the given expression −5x2y4+9x3y3+□{-5x^2y^4 + 9x^3y^3 + \square}, the last term is represented by the variable □{\square}. To create a polynomial in standard form, we need to choose a term that will complete the expression and make it a valid polynomial.

Option A: −xy5{-xy^5}

One possible option for the last term is −xy5{-xy^5}. This term has a degree of 1, which is lower than the degree of the other two terms. When added to the given expression, it will result in a polynomial with a degree of 5.

−5x2y4+9x3y3−xy5{-5x^2y^4 + 9x^3y^3 - xy^5}

This expression is a valid polynomial in standard form, with the terms arranged in descending order of exponents.

Option B: −3x2y4{-3x^2y^4}

Another possible option for the last term is −3x2y4{-3x^2y^4}. This term has the same degree as the first term, but with a negative coefficient. When added to the given expression, it will result in a polynomial with a degree of 2.

−5x2y4+9x3y3−3x2y4{-5x^2y^4 + 9x^3y^3 - 3x^2y^4}

This expression is also a valid polynomial in standard form, with the terms arranged in descending order of exponents.

Option C: −9x3y3{-9x^3y^3}

A third possible option for the last term is −9x3y3{-9x^3y^3}. This term has the same degree as the second term, but with a negative coefficient. When added to the given expression, it will result in a polynomial with a degree of 3.

−5x2y4+9x3y3−9x3y3{-5x^2y^4 + 9x^3y^3 - 9x^3y^3}

This expression is also a valid polynomial in standard form, with the terms arranged in descending order of exponents.

Conclusion

In conclusion, the last term of a polynomial plays a crucial role in determining the overall form of the expression. By choosing the right last term, we can create a polynomial in standard form. In this article, we explored three possible options for the last term of the given expression −5x2y4+9x3y3+□{-5x^2y^4 + 9x^3y^3 + \square} and identified three correct answers: −xy5{-xy^5}, −3x2y4{-3x^2y^4}, and −9x3y3{-9x^3y^3}. These options result in valid polynomials in standard form, with the terms arranged in descending order of exponents.

Final Answer

The three correct answers are:

  • −xy5{-xy^5}
  • −3x2y4{-3x^2y^4}
  • −9x3y3{-9x^3y^3}
    Frequently Asked Questions: Creating a Polynomial in Standard Form ====================================================================

In our previous article, we explored the process of selecting the right last term for the given expression −5x2y4+9x3y3+□{-5x^2y^4 + 9x^3y^3 + \square} and identified three correct options. In this article, we will answer some frequently asked questions related to creating a polynomial in standard form.

Q: What is the standard form of a polynomial?

A: The standard form of a polynomial is written with the terms arranged in descending order of exponents, with the highest degree term first.

Q: Why is the last term important in a polynomial?

A: The last term of a polynomial is the term with the lowest degree, and it plays a significant role in determining the overall form of the expression. It helps to complete the polynomial and make it a valid expression.

Q: How do I choose the right last term for a polynomial?

A: To choose the right last term, you need to consider the degree of the other terms in the polynomial. The last term should have a lower degree than the other terms, and it should be a valid term that can be added to the polynomial.

Q: What are some common mistakes to avoid when creating a polynomial in standard form?

A: Some common mistakes to avoid when creating a polynomial in standard form include:

  • Not arranging the terms in descending order of exponents
  • Not including the last term, which can make the polynomial invalid
  • Including a term with a higher degree than the other terms

Q: How do I check if a polynomial is in standard form?

A: To check if a polynomial is in standard form, you can follow these steps:

  • Arrange the terms in descending order of exponents
  • Check if the highest degree term is first
  • Check if the last term has a lower degree than the other terms

Q: What are some examples of polynomials in standard form?

A: Some examples of polynomials in standard form include:

  • x3+2x2−3x+1{x^3 + 2x^2 - 3x + 1}
  • 2x4−3x3+x2+1{2x^4 - 3x^3 + x^2 + 1}
  • x2+2xy+y2{x^2 + 2xy + y^2}

Q: Can I have a polynomial with no last term?

A: No, a polynomial cannot have no last term. The last term is an essential part of the polynomial, and it helps to complete the expression.

Q: Can I have a polynomial with a term that has a higher degree than the other terms?

A: No, a polynomial cannot have a term that has a higher degree than the other terms. The terms in a polynomial should be arranged in descending order of exponents.

Conclusion

In conclusion, creating a polynomial in standard form requires careful consideration of the last term. By choosing the right last term, you can create a valid polynomial that meets the standard form requirements. We hope this article has answered some of your frequently asked questions related to creating a polynomial in standard form.

Final Answer

The three correct answers are:

  • −xy5{-xy^5}
  • −3x2y4{-3x^2y^4}
  • −9x3y3{-9x^3y^3}